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DY: Fachverband Dynamik und Statistische Physik

DY 9: Statistical Physics far from Thermal Equilibrium I

DY 9.3: Vortrag

Montag, 9. März 2026, 10:00–10:15, ZEU/0160

Mutual linearity: A generic property of steady-state Markov networks — •Robin Bebon and Thomas Speck — Institute for Theoretical Physics 4, University of Stuttgart, Heisenbergstraße 3, 70569 Stuttgart, Germany

Nonequilibrium response theory has long sought universal principles to characterize the behavior of observables under external perturbations. While powerful tools exist near thermal equilibrium, general results far from equilibrium remain sparse and often rely on specific assumptions that severely limit their applicability, e.g., a specific parametrization of transition rates. In this work, we prove a remarkably simple, yet broadly applicable result: In a Markov network, any two steady-state probabilities remain linearly related when perturbing transition rates along a single edge of the network. This mutual linearity holds for every irreducible Markov network, arbitrarily far from equilibrium, and is independent of the chosen rate parametrization. As key implications, we demonstrate that the relative response of all states in the network is identical and show that analogous linear relations follow for a broad class of observables, including generic state-dependent and counting observables. Crucially, the coefficients that enter these linear relationships are empirically accessible, which makes our results not only conceptually significant but also provide a novel practical tool for inference and model validation in biological and chemical systems.

Keywords: Nonequilibrium response theory; Complex networks; Biological networks; Markov processes